The news was first reported by NFL Network.
The two-time Pro Bowler left Sunday's game against Arizona in the second quarter and did not return. He suffered the injury while coming out of the backfield, taking a pitch to his right. He made a cut and planted his foot, which is when he felt the pain in his right hamstring. He grabbed it and immediately jogged off to the sideline.
Martin had an MRI on Tuesday.
Charles Sims and newly signed Jacquizz Rodgers were pressed into duty after Martin's injury, and the Bucs mustered only 85 rushing yards against the Cardinals.? Jameis Winston had a career-high 52 passing attempts and four interceptions in the 40-7 blowout loss.
Martin was second in the NFL with 1,402 rushing yards in 2015, and he averaged 4.9 yards per carry.?He averaged 18 touches in 16 games, accounting for nearly 72 percent of the Bucs' rushing yards from running backs last year.
"When you take a top-level player out, you usually don't have exactly the same caliber player behind him, even though we're very high on Charles Sims," Bucs coach Dirk Koetter said Monday. "But yeah, it definitely hurts you. But that's the NFL. You're only healthy for one week and then you're hoping that you are fortunate enough to stay healthy the rest of the year. We didn't have good fortune in that department (Sunday), but this will be a new week."
Tampa Bay plays the Los Angeles Rams?at home on Sunday.
ESPN Staff Writer Jenna Laine contributed to this report.